Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74249We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundamental groups. Thus the topological fundamental group has the capacity to distinguish homotopy type when the Whitehead theorem fails.5 pages; minor improvementsAlgebraic TopologyGeneral Topology55P15Topological fundamental groups can distinguish spaces with isomorphic homotopy groupstext